My iPhone 5 keeps dropping Wi-Fi while streaming YouTube?

I'm the proud owner of an iPhone 5. Everything has been fine. The thing that's bugging me at the moment is the Wi-Fi.
I will be streaming a film over Wi-Fi and everything will be fine then I will look and see the 3G icon appear and realize that for the past 10 minutes I have been using 3G to stream my movie.
Now in the past that was not such a problem because I had unlimited Wi-Fi, but now I changed my plan and I only get 1GB a month and you can imagine how much streaming movies kills my allowance. So this has turned into quite a problem.
I'm not running an Jailbreaks or illegal streaming sites, it's like on YouTube and on TV catch up sites. I will be watching and then it just drops. It doesn't alert me to let me know the Wi-Fi has dropped and it doesn't automatically reconnect to the Wi-Fi either. The thing is I have checked my Wi-Fi and its perfectly fine. I have been on the internet on my PC at the same time and it has continued working without a hitch so it is something on the iPhone 5 that is wrong. So I really don't know what to do now.
Has anyone else had this and worked out a solution?

You might want to try changing your router to wep instead of wpa connection, wep is more compatible with connections so thats worth a try if the problem continues.